Question

If an object is rotating freely in space on its axis and suddenly its axis tilt changes then what will be the effect on its angular velocity or speed? Explain.

Answer 1

This is a condition which is called Torque-free precession , and it implies that no external moment (torque) is applied to the body when axis changes. In torque-free precession, the angular momentum is a constant, but the angular velocity vector changes orientation with time.

Angular Velocity changes but speed remains constant.


What makes this possible is a time-varying moment of inertia, or more precisely, a time-varying inertia matrix. The inertia matrix is composed of the moments of inertia of a body calculated with respect to separate coordinate axes (e.g. x, y, z). If an object is asymmetric about its principal axis of rotation, the moment of inertia with respect to each coordinate direction will change with time, while preserving angular momentum. The result is that the component of the angular velocities of the body about each axis will vary inversely with each axis' moment of inertia.